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Question

AM is a median of ABC. Then which of the following relation will always hold good?


A

AB+BC+CA = 2 AM

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B

AB+BC+CA > 2AM

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C

AB+BC+CA < 2AM

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D

AB+BC+CA = AM

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Solution

The correct option is B

AB+BC+CA > 2AM


Sum of lengths of any two sides of a triangle is always greater than the third side.
Hence, AB + BM > AM;
AC + CM > AM
Adding the above inequalities gives,
AB + BC + CA > 2AM


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